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Title: A majorization-minimization approach to design of power distribution networks

Abstract

We consider optimization approaches to design cost-effective electrical networks for power distribution. This involves a trade-off between minimizing the power loss due to resistive heating of the lines and minimizing the construction cost (modeled by a linear cost in the number of lines plus a linear cost on the conductance of each line). We begin with a convex optimization method based on the paper 'Minimizing Effective Resistance of a Graph' [Ghosh, Boyd & Saberi]. However, this does not address the Alternating Current (AC) realm and the combinatorial aspect of adding/removing lines of the network. Hence, we consider a non-convex continuation method that imposes a concave cost of the conductance of each line thereby favoring sparser solutions. By varying a parameter of this penalty we extrapolate from the convex problem (with non-sparse solutions) to the combinatorial problem (with sparse solutions). This is used as a heuristic to find good solutions (local minima) of the non-convex problem. To perform the necessary non-convex optimization steps, we use the majorization-minimization algorithm that performs a sequence of convex optimizations obtained by iteratively linearizing the concave part of the objective. A number of examples are presented which suggest that the overall method is a good heuristicmore » for network design. We also consider how to obtain sparse networks that are still robust against failures of lines and/or generators.« less

Authors:
 [1];  [1]
  1. Los Alamos National Laboratory
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1000948
Report Number(s):
LA-UR-10-02039; LA-UR-10-2039
TRN: US201101%%727
DOE Contract Number:  
AC52-06NA25396
Resource Type:
Conference
Resource Relation:
Conference: 49th IEEE Conference on Decision and Control ; December 15, 2010 ; Atlanta, GA
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; ALGORITHMS; ALTERNATING CURRENT; CONSTRUCTION; DESIGN; HEATING; OPTIMIZATION; POWER DISTRIBUTION

Citation Formats

Johnson, Jason K, and Chertkov, Michael. A majorization-minimization approach to design of power distribution networks. United States: N. p., 2010. Web.
Johnson, Jason K, & Chertkov, Michael. A majorization-minimization approach to design of power distribution networks. United States.
Johnson, Jason K, and Chertkov, Michael. 2010. "A majorization-minimization approach to design of power distribution networks". United States. https://www.osti.gov/servlets/purl/1000948.
@article{osti_1000948,
title = {A majorization-minimization approach to design of power distribution networks},
author = {Johnson, Jason K and Chertkov, Michael},
abstractNote = {We consider optimization approaches to design cost-effective electrical networks for power distribution. This involves a trade-off between minimizing the power loss due to resistive heating of the lines and minimizing the construction cost (modeled by a linear cost in the number of lines plus a linear cost on the conductance of each line). We begin with a convex optimization method based on the paper 'Minimizing Effective Resistance of a Graph' [Ghosh, Boyd & Saberi]. However, this does not address the Alternating Current (AC) realm and the combinatorial aspect of adding/removing lines of the network. Hence, we consider a non-convex continuation method that imposes a concave cost of the conductance of each line thereby favoring sparser solutions. By varying a parameter of this penalty we extrapolate from the convex problem (with non-sparse solutions) to the combinatorial problem (with sparse solutions). This is used as a heuristic to find good solutions (local minima) of the non-convex problem. To perform the necessary non-convex optimization steps, we use the majorization-minimization algorithm that performs a sequence of convex optimizations obtained by iteratively linearizing the concave part of the objective. A number of examples are presented which suggest that the overall method is a good heuristic for network design. We also consider how to obtain sparse networks that are still robust against failures of lines and/or generators.},
doi = {},
url = {https://www.osti.gov/biblio/1000948}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 2010},
month = {Fri Jan 01 00:00:00 EST 2010}
}

Conference:
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